Mean-Variance QTL Mapping on a Background of Variance Heterogeneity

Abstract

Most QTL mapping approaches seek to identify "mean QTL", genetic loci that influence the phenotype mean, after assuming that all individuals in the mapping population have equal residual variance. Recent work has broadened the scope of QTL mapping to identify genetic loci that influence phenotype variance, termed "variance QTL", or some combination of mean and variance, which we term "mean-variance QTL".Even these approaches, however, fail to address situations where some other factor, be it an environmental factor or a distant genetic locus, influences phenotype variance. We term this situation "background variance heterogeneity" (BVH) and used simulation to explore its effects on the power and false positive rate of tests for mean QTL, variance QTL, and mean-variance QTL. Specifically, we compared traditional tests, linear regression for mean QTL and Levene's test for variance QTL, with tests more recently developed, namely Cao's tests for all three types of QTL, and tests based on the double generalized linear model (DGLM), which, unlike the other approaches, explicitly models BVH. Simulations showed that, when used in conjunction with a permutation procedure, the DGLM-based tests accurately control false positive rate and are more powerful than the other tests. We also discovered that the rank-based inverse normal transform, often used to corral unruly phenotypes, can be used to mitigate the adverse effects of BVH in some circumstances. We applied the DGLM approach, which we term "mean-variance QTL mapping", to publicly available data on a mouse backcross of CAST/Ei into M16i and, after accommodating BVH driven by father, identified a new mean QTL for bodyweight at three weeks of age. KEYWORDS QTLmapping, background

Genotype-by-environment interactions inferred from genetic effects on phenotypic variability in the UK Biobank

“…We observed no inflation in FPR for the Levene’s test under the null (i.e., no vQTL effect) regardless of the skewness or kurtosis of the phenotype distribution or the presence or absence of the SNP effect on mean (Supplementary Figure 1a). These findings are in line with the results from previous studies 16,20,30 that demonstrate the Levene’s test is robust to the distribution of phenotype. The FPR of the Bartlett’s test or DGLM was inflated if the phenotype distribution was skewed or heavy-tailed (Supplementary Figure 1a).…”

“…We found that the FPR of the Levene’s test was well-calibrated across all simulation scenarios whereas the other methods showed an inflated FPR if the phenotype distribution was skewed or heavy-tailed under the null hypothesis (i.e., no vQTL effect), despite that the Levene’s test appeared to be less powerful than the other methods under the alternative hypothesis in particular when the per-variant vQTL effect was small (Figure 2 and Supplementary Figure 1). Parametric bootstrap or permutation procedures have been proposed to reduce the inflation in the test-statistics of DGLM and LRT-based method, both of which are expected to be more powerful than the Levene’s test 28,30 , but bootstrap and permutation are computationally inefficient and thus not practically applicable to biobank data such as the UKB. In addition, we observed inflated FPR for the Levene’s test in the absence of vQTL effects but in the presence of QTL effects if the phenotype was transformed by logarithm transformation or RINT.…”

vqtl: An R Package for Mean-Variance QTL Mapping

“…In the case of genetic factors, they can be mapped, as illustrated in one companion article (Corty et al 2018). In the case of covariates, they can be accommodated, which can increase power and improve false positive rate control, as illustrated in another companion article (Corty and Valdar 2018).…”

“…To calculate the empirical, FWER-controlled p -value of each test at each locus we advocate use of a permutation procedure (Corty and Valdar 2018). Like previous work on permutation-based thresholds for genetic mapping (Churchill and Doerge 1994; Carlborg and Andersson 2002), this procedure sidesteps the need to explicitly estimate the effective number of tests.…”

“…Our approach, which we term “mean-variance QTL mapping”, is based on a double generalized linear model (DGLM) (Smyth 1989), following the proposed use in this context by Rönnegård and Valdar (2011). In the first of two companion articles, we characterize the method and competitors in the setting where variance heterogeneity is driven by a background factor, such as sex, batch or housing, and show that modeling these (external) variance effects improves power to detect mQTL, vQTL and mvQTL (Corty and Valdar 2018). In the second companion paper, we demonstrate the approach on two existing datasets and discover new mQTL and vQTL (Corty et al 2018).…”